1

The following paper has been accepted for publication in the Journal of ChemicalPhysics (February 2001). After the paper is published, it will be found at the following

URL: http://ojps.aip.org/jcpo/

Forced Rayleigh Scattering Studies of Tracer Diffusion in a Nematic

Liquid Crystal: The Relevance of Complementary Gratings

Daniel R. Spiegel, Alexis L. Thompson, and Wesley C. CampbellDepartment of Physics, Trinity University, San Antonio, TX 78212-7200

Abstract

We have employed forced Rayleigh scattering (FRS) to study the diffusion of an azo

tracer molecule (methyl red) through a nematic liquid crystal (5CB). This system was

first investigated in an important study by Hara et al. (Japan. J. Appl. Phys. 23, 1420

[1984]). Since that time, it has become clear that the presence of complementary ground-

state and photoproduct FRS gratings can result in nonexponential profiles, and that

complementary-grating effects are significant even when “minor” deviations from

exponential decay are observed. We have investigated the methyl red/5CB system in

order to evaluate the possible effects of complementary gratings. In the isotropic phase,

we find that the presence of complementary gratings results in a nonmonotonic FRS

signal, which significantly changes the values inferred for the isotropic diffusion

coefficients. As a result, the previously reported discontinuity at the nematic/isotropic

transition temperature (TNI) is not present in the new data. On the other hand, in the

nematic phase, the new experiments largely confirm the previous observations of single-

exponential FRS decay and the non-Arrhenius temperature dependence of the nematic

diffusion coefficients close to TNI. Finally, we have also observed that the decrease in

the diffusion anisotropy with increasing temperature can be correlated with the 5CB

nematic order parameter S(T) over the full nematic temperature range.

2

INTRODUCTION

Many of the most fascinating properties of nematic liquid crystals (NLCs) derive

from the simultaneous presence of flow and a non-zero orientational order parameter: a

molecule within the NLC mesophase will undergo translational diffusion while

maintaining (on average) a preferred orientation.1 It is thus rather unfortunate that some

of the most fundamental aspects of translational diffusion within NLCs are still not well

understood, in spite of the impressive array of experimental, simulation, and theoretical

methods that have been brought to bear on the problem.2-16 On the experimental side,

reports on NLC diffusion coefficients obtained by different methods have displayed

significant discrepancies, and even results reported by different laboratories employing the

same method often display marked disagreement.4,7 The lack of consistency was severe

enough to be termed an “experimental dilemma” in a recent review.7 These difficulties

have largely prevented a rigorous comparison of experimental results with fundamental

theories proposed for NLC molecular diffusion,17-20 and it is clear that experimental

accuracies must be improved if such comparisons are to be realized.

One very useful experimental method for studies of diffusion in liquid crystals is

forced Rayleigh scattering (FRS),21-31 which was first employed for tracer diffusion in

NLCs by Hervet et al. in 1978.21 FRS is a transient grating method that is particularly

well-suited for studies of NLC dynamics for three reasons. First, FRS permits real-time

measurements of diffusion in the specific direction selected by the grating wavevector,

which readily enables direct investigations of the diffusion anisotropy. Second, the

fundamental length scale of the FRS experiment (i.e. the grating spacing, which is

3

typically on the order of several microns) matches the intrinsic length scale at which

mesomorphic fluids exhibit many of their most interesting properties.1 Finally, FRS

allows measurements at a spatial resolution determined by the diameter of the laser

beams, which can easily be reduced to ~ 10d (where d is the grating spacing) if

desired.32,33

In this paper we wish to consider a possible means for significant improvements in

the accuracy of FRS studies on NLC systems. While mass-diffusion FRS signals were

initially modeled as simple exponential functions,21 it was later realized that an FRS

signal results in general from a difference of two exponential decays due to

“complementary” out-of-phase modulations in the ground-state and photoproduct

populations.34,35 A series of recent papers36-38 have outlined the changes in the

interpretation of FRS profiles necessitated by the presence of complementary gratings.

These developments have led us to reexamine a pertinent liquid crystal system, first

studied with FRS before the complementary grating model was set forth, that has

displayed some surprising results. Specifically, we use FRS to investigate the azo dye

molecule methyl red (MR, 2-[4-(dimethylamino)phenylazo ]benzoic acid) diffusing

though a cyanobiphenyl NLC (5CB, 4-n-pentyl-4/-cyanobiphenyl). The first FRS

investigations on the MR/5CB system were carried out in an important study by Hara and

co-workers22 in 1984. This early work showed several intriguing features, including a

non-Arrhenius temperature dependence in the nematic-phase diffusion coefficients near

the nematic-isotropic transition temperature (TNI), and an unexpected discontinuity (a

positive jump) in the diffusion coefficient at TNI. A considerably larger positive jump at

TNI was reported for MR in MBBA in the same publication, and later papers showed

4

positive jumps at TNI for MR in a number of other mesomorphic solvents, including other

nCB compounds (n = 6 - 9), 4O.8, and 8OCB.39-42 To explain the nematic/isotropic

discontinuity, it was proposed41 that tracer diffusion through the nematic phase could be

envisioned as a “dressed” process, in which the mobility of the tracer was reduced due to

local distortions in the nematic continuum generated by the tracer movement, in a manner

somewhat analogous to polaron motion in the solid state. The data submitted in the

current report, interpreted in the context of the complementary grating model, largely

confirm the important observation by Hara et al. of non-Arrhenius diffusion in the 5CB

nematic phase; however, in the 5CB isotropic phase we observe a distinctly

nonexponential decay, which significantly changes the values obtained for the isotropic

diffusion coefficients. We will discuss the implications of these findings.

FRS is a tracer diffusion technique, in the sense that it measures the self-velocity

correlations of detected dilute “tracer” dye molecules within a host solvent. MR has been

frequently chosen as a tracer dye in liquid crystal systems due to its convenient

photochromic properties and the similarity between its structure and that of liquid crystal

molecules containing a two-phenyl-ring core.21,22,25,32,39-44 However, here we make no a

priori assumptions that tracer diffusion of MR will mimic exactly the self-diffusion of the

5CB solvent molecules, since the chemical properties of MR and 5CB are certainly

different. Indeed, using FRS, Urbach et al.32 and more recently Ohta and co-workers45

have reported that MR-tracer diffusion is considerably slower than the self-diffusion of

the liquid crystalline solvent molecules in nematic MBBA. It has been argued that, in

NLCs, the self-diffusion of the solvent molecules and the tracer diffusion of a probe

molecule of similar size will in general show the same basic features, but the anisotropy

5

will be reduced for the latter.4 Keeping this caveat in mind, it nonetheless remains clear

that tracer diffusion is a very helpful tool for improving the understanding of NLC

dynamics. FRS tracer diffusion in particular provides a very direct experimental probe of

the anisotropic micron-scale dynamics of NLC fluids, which remains an area with many

open questions.

EXPERIMENTAL PROCEDURES

MR and 5CB were purchased from Aldrich and EM Industries, respectively, and

were used as received. MR/5CB solutions were prepared for FRS studies at a

concentration of 0.1 wt %. The nematic-isotropic transition temperature for the 0.1%

solution was found to be (34.2 ± 0.2) oC, which was not (within uncertainty) different

from the measured transition temperature for the neat 5CB. The MR/5CB NLC samples

were prepared by confining the mesophase between two clean microscope slides. The

slides were separated by 34-gauge copper wire strands, resulting in samples with a

nominal thickness of 150 µm. For studies of the temperature dependence of the diffusion

coefficient in the nematic phase, the slides were first treated with an aqueous solution of

poly(vinyl alcohol) (PVA) following standard procedures,46 and then rubbed with soft

paper along a specific direction to achieve planar alignment. The use of rubbed PVA

coatings resulted in nearly single-domain nematic samples: at most, only a few small

disclinations were observed, and these could be easily avoided when choosing the small

spot (roughly 4 mm2) to be examined with the FRS apparatus. For studies of the

isotropic phase at temperatures greater than 36 oC, the slides were cleaned but not coated

with PVA. The MR/5CB solution was sealed within the cell using a silicone adhesive.

6

In a FRS experiment, two interfering pump beams are used to produce a periodic

fringe pattern within a sample containing a small concentration of a photochromic dye.

Absorption of the pump-beam photons creates a modulation in the photoproduct and

(hence) the ground-state dye population. The maxima in the ground-state population

profile are coincident with the minima in the complementary photoproduct distribution.

The decay of the induced modulation patterns due to diffusion can be monitored with a

Bragg-diffracted probe beam. Since the ground-state and photoproduct molecules do not

diffuse at identical rates, the intensity of a Bragg-diffracted homodyne-detected probe

beam will decay with time according to

V(t) = (A1 exp[-r1t] – A2 exp[-r

2t])2

(1)

where the Ai and the ri represent the amplitudes and decay constants, respectively,

associated with the ground-state and photoproduct gratings. The negative sign arises

because of the 180o spatial phase shift between the two gratings. Nearly single-

exponential decay is a special case of Eq. (1), and it should be kept in mind that,

according to Eq. (1), highly nonexponential (indeed, nonmonotonic) profiles are possible

for an arbitrarily small difference between the rate constants ri if the difference between

the amplitudes Ai is also small.37 Eq. (1) is strictly correct only for pure phase gratings.

In the more general case of “mixed” amplitude/phase gratings, the decay of a Bragg-

diffracted probe is given by34,38

7

V(t) = A1 exp[-r1t] – e

i ∆ φ A2 exp [-r

2t]

2(2)

where ∆φ is the difference between the optical phase shifts of the electric fields diffracted

from the two gratings. The phase difference ∆φ will be nonzero whenever a portion of

the probe beam is absorbed within the sample.47

Azobenzene derivatives (such as MR) undergo a trans ⇒ cis isomerization when

excited by photons within the visible/UV absorption band. The FRS grating contrast is

provided by the difference in the (complex) index of refraction between the trans and the

cis species. The FRS apparatus employed for the current studies utilizes a 488-nm pump

beam and a 633-nm probe beam incident at powers of 12 mW (total) and 5 mW,

respectively. Since this apparatus has been described in previous reports,36,37 the

discussion here is limited to several new features relevant to studies of NLCs. The

liquid-crystal sample holder consists of a machined aluminum retainer mounted to a

rotation stage, which allows the director to be oriented parallel or perpendicular to the

horizontal grating wavevector q. An 8-mm-diameter hole cut though the holder and the

rotation stage allows passage of the laser beams. The stage is attached to a copper block

soldered to copper pipes to permit water-flow temperature control (Neslab RTE-111).

The sample temperature was calibrated in a separate run using a thermocouple junction

mounted between two microscope slides and placed at the position usually occupied by

the sample. The precision of the temperature control was limited to about ± 0.2 oC due to

fluctuations in room temperature. The pump beam polarization was vertical (to about

± 1o). Following Hara et al.,22 the polarization of the probe beam was rotated (using a

8

633-nm half-wave plate) so that the probe polarization was always parallel to the nematic

director, and a spatial filter and a dichroic polarizer with its transmission axis aligned

parallel to the incident probe-beam polarization were placed between the sample and the

detector to reduce detection of scattered light. The probe-beam polarization was vertical

in the isotropic phase. Pump beam exposure times (2 – 7 ms) were controlled using a

shutter. Signals were acquired and averaged for 50 - 300 single shots on a digital storage

oscilloscope (DS0). Reports in the literature37,48 have clearly demonstrated the need for

proper separation of the heterodyne and homodyne baseline components for accurate

FRS results. For the present studies, the heterodyne baseline contribution (i.e., the

crossterm arising from the mixing of light diffracted from the pump-induced gratings

with light scattered from stationary defects) was eliminated by passing one of the pump

beams through a 488-nm half-wave plate which, when rotated through 90o, introduces a

180o shift between the phase of the probe light diffracted from the gratings and the phase

of the probe light scattered from stationary defects. The sum of the two FRS profiles

acquired before and after this phase shift is then a pure homodyne signal.48 All data were

acquired using this procedure.

One concern that arises with the MR/5CB system involves the potential effects of

the photoproduct cis population on the mesoscopic properties of the NLC: since the cis

state of MR is non-planar, photoexcitation of a MR molecule might be expected to lead to

a local disruption of the nematic ordering.45,49-52 To investigate possible unintended

effects due to dye photoexcitation, we measured the FRS rate constant as a function of

the pump-beam intensity in the nematic phase at a temperature of 33.9 oC with

9

q2 = 2.47 × 10

8 cm

-2. Attenuation of the pump beam by up to a factor of 14 did not

result in a measurable change in the FRS rate constants for diffusion parallel or

perpendicular to the director, implying that even an order-of-magnitude change in the cis

population does not measurably affect our diffusion-coefficient results.

RESULTS AND DISCUSSION

FRS profiles for diffusion parallel and perpendicular to the director in the nematic

phase at 33.9 oC, along with a profile for the isotropic phase at 35.6

oC, are shown in Fig.

1. The three profiles, acquired on the same day using the same PVA-coated sample,

appear qualitatively similar using a DSO sensitivity in which the entire profile is acquired

(Fig. 1a). If the DSO sensitivity is increased, however, the isotopic profile is seen to

contain a secondary maximum, as shown in Fig. 1b. The secondary peak is quite small

(less than 0.1% of the maximum signal), but is observed consistently at all grating

wavevectors and temperatures investigated in the isotropic phase. Evidently, the

isotropic signal is an example of a “decay-grow-decay” type of profile (with two times at

which the derivative V /(t) vanishes) that has appeared frequently in the FRS

literature,27,29,31,38,53,54 including at least one case of a smectic mesophase.25

The existence of profiles with zero, one, or two times at which the derivative V /(t) is

zero follows directly from Equations (1) or (2) above. Care must be exercised in fitting

Equations (1) or (2) to experimental profiles via nonlinear regression, since it has been

shown that such fits are in general not unique.33,37,38 To avoid such problems, we

adopted the approach recently suggested by Park et al.,38 who pointed out that in many

10

cases the average FRS rate constant rav = (1/2)(r1 + r2) can be determined uniquely and

without difficulty from nonexponential profiles by expressing the FRS signal (Eq. [2]) in

the simple form

V(t) ≈ (at2 + bt + c) exp(-2 rav t) . (3)

The constant coefficients a, b, and c can be expressed in terms of (r2 – r1), ∆φ, and the

Ai. Equation (3) is obtained from a Taylor series expansion of Eq. (2) about the time

t0 = (r2 - r1)-1{ln(A2/A1) + i ∆φ}, and represents a useful approximation for

nonmonotonic profiles whenever the fractional differences (A2 - A1)/A1 and (r2 - r1)/r1

are not very large (as expected for azo dyes),35,55 and ∆φ << 1 rad. Equation (3) has four

unknown parameters (one less than Eq. [2]), three of which appear linearly; thus, Eq. (3)

is expected to be far less susceptible to the problems with non-unique fits reported using

Equations (1) or (2).27,33,38,56 For pure phase gratings (∆φ = 0), in which case t0 is real

and represents the time at which the signal V(t) is zero, Eq. (3) reduces to

V(t) ≈ a / (t - t0)2 exp(-2 rav t) (4)

which contains three unknown parameters (one less than Eq. [1]). In Fig. 2 it can be seen

that the minimum in the isotropic profile does not reach the baseline, which demonstrates

that ∆φ ≠ 0 due to a small amount of probe beam absorption within the long-wavelength

11

tail of the visible MR absorption band. We therefore fit all isotropic profiles to Eq. (3) to

obtain rav. An example of a fit to Eq. (3) is also shown in Fig. 2.

Turning to the nematic profiles, it is important to determine if single-exponential fits

are appropriate in this case. It has been shown that,37 when the photoproduct and ground-

state rate constants differ by a small amount, forcing a single-exponential fit to a

monotonic FRS profile can lead to significant errors, since the semi-log slope

rexp = (-1/2) d(ln[V])/dt does not represent a physically useful FRS rate constant unless

the dimensionless curvature K2/(K1)2 is zero within experimental error. K1 and K2 are

the first and second derivatives of (1/2)ln(V[t]) at t = 0 and can be used to provide

estimates of the first and second cumulants, respectively, of the FRS decay.57 We

applied second-order polynomial fits to multiple profiles to obtain averages of K2/(K1)2

at two different temperatures with the director orientated either perpendicular or parallel

to the grating wavevector. In each case, four signal profiles obtained at different grating

wavevectors were each fit over the time interval for which V(t) varied from 90% down to

40% of its maximum value. (The top 10% of the profile was not included in the fit to

allow time for the much faster thermal-grating decay.)37 At a temperature of 33.8 oC, we

obtained, using ±1σ uncertainties, ⟨K2/(K1)2⟩

⊥ = 0.13 ± 0.09 and

⟨K2/(K1)2⟩

= -0.1 ± 0.1. At a temperature of 25.9

oC, we measured

⟨K2/(K1)2⟩⊥ = -0.08 ± 0.08 and ⟨K2/(K1)2

⟩ = 0.003 ± 0.07. Thus the curvature ratio is

zero within uncertainty, which validates quantitatively the application of single-

12

exponential fits to the nematic data and implies that the semi-log slope is equal (within

uncertainty) to the rate constant rav.37 All nematic rate constants were then obtained

using single-exponential fits over the time interval for which V(t) varied from 90% down

to 2% of its maximum value.

Examples of rate constants obtained from single-exponential fits to the nematic

profiles, and from fits to Eq. (3) for the isotropic profiles, are shown as a function of q2 in

Fig. 3. All diffusion coefficients in this report were obtained from the slope of such plots

using 4 different values of q2. In Fig. 4 we show the diffusion coefficient as a function of

temperature for diffusion parallel and perpendicular to the director in the nematic phase,

along with the diffusion coefficient in the isotropic phase. From sample-to-sample

variations in the rate constants we estimate the maximum error in the diffusion

coefficient to be ± 3% in the nematic phase and ± 6% in the isotropic phase. The

temperature dependence is arguably of the Arrhenius type for the isotropic phase and in

the low-temperature (T < 30 oC) region of the nematic phase, although certainly any

assignment of an “Arrhenius” dependence over the rather narrow temperature regions

studied must be made with due caution. Table I reports the corresponding isotropic

activation energy ∆Eiso and the nematic-phase activation energies ∆E and ∆E⊥. There is

no obvious break in the temperature dependence at the nematic-isotropic transition

temperature: D and Diso are essentially continuous across TNI.

As the temperature approaches TNI in the nematic phase, the behavior is clearly non-

Arrhenius. Although both D and D⊥ display a decreasing slope as T à TNI, the effect is

13

more dramatic for D, so that the anisotropy ratio D/D⊥ decreases as the phase

transition is approached. The variation in D/D⊥ can be exhibited in a more direct

fashion by plotting this ratio as a function of the nematic order parameter S(T). To obtain

the latter, we use S(T) as derived by Sherrell and Crellin58 from their measurements of

the anisotropy in the 5CB nematic-phase magnetic susceptibility, which were later

recommended by Ahlers59 as the best available values. D/D⊥ is plotted as a function of

S(T) for the full nematic temperature range in the inset of Fig. 4. As expected from first

principles,18,19 the diffusion anisotropy measured using FRS increases as the 5CB

nematic order parameter increases, although improved precision will certainly be

necessary before the correct quantitative relation between these two quantities can be

identified with confidence.

We may now compare the current work to a previous study by Hara et al.,22 who

also carried out FRS studies on 0.1% MR-5CB samples confined between rubbed PVA-

treated slides. As in the current study, rate constants in the nematic phase were obtained

using single-exponential fits. For comparison, the nematic activation energies and the

values of D and D⊥ at 25 oC obtained by Hara et al. are included along with the results

of the present work in Table I. There is good agreement in the values of the diffusion

coefficients at 25 oC. On the other hand, Hara et al. obtained activation energies for

parallel and perpendicular diffusion coefficients that differed by about 80%, while the

two activation energies are nearly equal for the current investigations. It is worth noting,

however, that the scatter in the diffusion coefficient vs. temperature measurement of Hara

et al. is larger than that of the present study, and that the average of the parallel and

14

perpendicular activation energies reported previously is close to the average obtained in

the current study. Hara et al. carefully noted a decrease in the slope of D as the

temperature approached TNI, and Figure 6 of their paper shows a possible decrease in the

slope of D⊥ in this temperature region. The present results largely confirm these

important observations (at a somewhat higher internal precision), and also show that the

non-Arrhenius dependence can be correlated with the nematic order parameter.

In their studies of the isotropic MR/5CB phase, Hara et al. also fit the FRS profiles

to single-exponential decays. The secondary peak shown in Fig. 1b of the current report

was apparently not detected, presumably because of its small amplitude relative to the

maximum signal level. (It should be noted that there was no reason to expect a secondary

maximum when the Hara et al. work was carried out, since the significance of

complementary FRS gratings had not yet been identified.34,35) The data of Hara et al.

show (in their words) a “discontinuous jump” in the diffusion coefficient at TNI, with

Diso(TNI) exceeding D(TNI) by ~ 30%. The current studies treat the FRS signals in the

context of the complementary grating model, yielding a smaller value for Diso at TNI that

is (within error) nearly continuous with D, along with an isotropic activation energy

∆Eiso equal to about 2/3 of the value obtained previously (see Table I). Thus it is

apparent that the unexpected discontinuity at TNI is not observed when the

complementary grating characteristics of the FRS signals are accounted for. It is not

surprising that the isotropic diffusion coefficients obtained in the previous investigation

are consistently larger than those measured in the current study, since it is easily shown

that, for nearly-pure phase gratings, the rate constant rexp = (-1/2) d(ln[V])/dt extracted by

15

fitting a decay-grow-decay FRS profile to a single exponential function will always be

larger than either r1 or r2.37 The rather unremarkable transition from nematic to isotropic

diffusion evident in Fig. 4 implies that it is not necessary to invoke a hypothesis

involving “dressed” polaron-like tracer diffusion within the 5CB nematic phase. As

noted above, nematic/isotropic diffusion discontinuities have been reported in FRS

studies for MR in other NLC systems.39-42 Although the current experiment involves only

5CB, it is possible that the nematic/isotropic discontinuities reported for these other

systems could also be related to complementary grating effects. In any case, it is clear

that complementary grating considerations are important for accurate FRS studies of

dynamics within liquid crystals.

CONCLUSIONS

New FRS studies carried out using the complementary grating model to interpret

data obtained at higher sensitivity confirm the non-Arrhenius behavior reported

previously for MR in nematic 5CB. We have also found that the diffusion anisotropy

ratio D/D⊥ can be correlated with the nematic order parameter S(T) over the full nematic

temperature range. In the isotropic phase, we have observed a decay-grow-decay FRS

profile, resulting in new values for the isotopic diffusion coefficient and its activation

energy that are significantly lower than the previous values; this in turn removes the

previously reported diffusion anomaly at the nematic-isotropic phase transition. Our

results highlight the importance of accounting for complementary grating effects for

accurate FRS measurements in liquid-crystal systems.

16

ACKNOWLEDGMENTS

We gratefully acknowledge Dr. Taihyun Chang for his careful critique of the

manuscript, and we thank Dr. Thomas Moses and Dr. Benjamin Plummer for very useful

discussions. We are grateful to Mr. Tom Defayette for his extraordinary dedication and

expertise in the machine shop and the laboratory, to Mr. Richard Helmer for his highly

valuable contributions to the electronics, and to Mr. Timothy Gilheart and Mr. Dustin

Ragan for their assistance. Finally, we express our appreciation to the anonymous

reviewer, whose careful critique resulted in (we believe) significant improvements to the

clarity of the manuscript. The Trinity forced Rayleigh scattering laboratory is funded by

a grant from the National Science Foundation (RUI CHE-9711426).

17

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21

Table I. Diffusion of Methyl Red in 5CB. For the present work, activation energies in

the nematic phase are obtained for T < 30 oC (see Fig. 4). The results of Hara et al. were

published in Japan. J. Appl. Phys. 23, 1420 (1984).

Diffusion Constant Activation Energy(× 10

-7 cm

2/s) (kJ/mol)

D(25 oC) D⊥(25

oC) ∆E ∆E⊥ ∆Eiso

Present work 2.3 ± 0.1 1.5 ± 0.1 28 ± 1 31 ± 2 36.1 ± 0.3

Hara et al. 2.3 1.4 22 40 54

22

Figure Captions

Fig. 1. FRS signals obtained in MR/5CB samples at q2 = 5.50 × 107 cm

-2. Profiles are

displayed with the director oriented perpendicular (⊥) and parallel ( || ) to the grating

wavevector in the nematic phase at 33.9 oC, along with a profile in the isotropic (“iso”)

phase at 35.6 oC. (a) Full profiles, with horizontal and vertical offsets added for clarity.

To avoid detector saturation, the perpendicular and parallel nematic signals were

attenuated by 75% and 30%, respectively, using neutral density filters placed between the

sample and the detector. (b) The signal obtained at an increased oscilloscope sensitivity

(1 mV/division), with no additional changes. Horizontal and vertical offsets have been

added for clarity. It is apparent that the isotropic profile is nonmonotonic. (c) Logarithm

of the signals shown in parts (a) and (b). Vertical offsets have been added to the

logarithmic profiles for clarity. The smaller-size data points were obtained at the higher

oscilloscope sensitivity.

Fig. 2. A FRS profile obtained in the isotropic phase at a temperature of 34.8 oC using a

grating wavevector with q2 = 7.29 × 10

7 cm

-2. For clarity, only 25% (every fourth point)

of the data have been plotted. A fit to Eq. (3) (solid line) yields a = 229 V/s2,

b = - 48.9 V/s, c = 2.61 V, and rav = 23.7 Hz. The residuals (with every fourth point

plotted) are shown in the inset.

23

Fig. 3. Plots of the rate constant as a function of the square of the grating wavevector. In

the upper plot, the nematic rate constants, measured with the director oriented parallel ( || )

and perpendicular (⊥) to the grating wavevector, were obtained from simple exponential

fits. In the lower plot, the rate constants in the isotropic phase were obtained from fits to

Eq. (3).

Fig. 4. Tracer diffusion coefficients for MR in 5CB as a function of temperature in the

nematic and isotropic phases. The inset shows the ratio D/D⊥ as a function of the 5CB

nematic order parameter S(T) for the full nematic temperature range.

0

1

2

3

⊥

(a)

iso||

0.0 0.1 0.2 0.3

-10

-5

0

5

Fig. 1 Spiegel et al. JCP

(c)

⊥||

ln[V(t)] + Offset

iso

Time (s)0.0 0.4 0.8 1.2

0.000

0.005

0.010

iso||⊥

(b)

V(t

) (V

olts

)

Time (s)

0.0 0.2 0.4

0.0

0.5

1.0

Fig. 2 Spiegel et al. JCP

Time (s)

Res

idua

ls (µ

V)

V(t

) (

mV

)

Time (s)

0.0 0.2 0.4-40-20

02040

0 2x107 4x107 6x107 8x1070

10

20

30

riso

Fig 3 Spiegel et al. JCP

T = 42.1 oC

r||

Rat

e (H

z)

q2 (cm-2)

0 1x108 2x108 3x108020406080

T = 27.5 oC

r⊥

Rat

e (H

z)

q2 (cm-2)

3.35 3.30 3.25 3.20 3.1511

2

3

456

Diso

D⊥

D||

S(T)

Fig. 4 Spiegel et al. JCP

Temperature (oC)4540353025

D

iffus

ion

Coe

ffici

ent (

x 10

-7 c

m2 /s

)

Inverse Temperature (x 10-3 K-1)

0.4 0.61.3

1.4

1.5

1.6D

||/D

⊥